1. Field of the Invention(s)
Embodiments discussed herein are directed to topological data analysis using at least one function representable as a matrix function and more particularly, utilizing metric matrix functions for clustering data points projected in a covered reference space for scale topological analysis.
2. Related Art
As the collection and storage of data has increased, there is an increased need to analyze and make sense of large amounts of data. Examples of large datasets may be found in financial services companies, oil exploration, insurance, health care, biotech, and academia. Unfortunately, previous methods of analysis of large multidimensional datasets tend to be insufficient (if possible at all) to identify important relationships and may be computationally inefficient.
In order to process large datasets, some previous methods of analysis use clustering. Clustering often breaks important relationships and is often too blunt an instrument to assist in the identification of important relationships in the data. Similarly, previous methods of linear regression, projection pursuit, principal component analysis, and multidimensional scaling often do not reveal important relationships. Further, existing linear algebraic and analytic methods are too sensitive to large scale distances and, as a result, lose detail.
Even if the data is analyzed, sophisticated experts are often necessary to interpret and understand the output of previous methods. Although some previous methods allow graphs that depict some relationships in the data, the graphs are not interactive and require considerable time for a team of such experts to understand the relationships. Further, the output of previous methods does not allow for exploratory data analysis where the analysis can be quickly modified to discover new relationships. Rather, previous methods require the formulation of a hypothesis before testing.